Discussion

A certain brand of computer can be bought with or without a hard drive. The computer with the hard drive costs 2,900 dollars. The computer without the hard drive costs 1,950 dollars more than the hard drive alone. What is the cost of the hard drive?
(A)   400
(B)...
(C)...
(D)...
(E)...
(F)...
*This question is included in Nova Math - Problem Set BB: Miscellaneous Problems, question #1

The solution is

Posted: 08/01/2012 07:52
There is a difference of 950 here. How is 475 the answer? No matter which way I try and solve this I can't not understand this.
Posted: 08/01/2012 14:47
Let's set up the problem. That's 90% of the solving.

Cost of hard drive = HD
Computer with hard drive = CHD
Computer without hard drive = CXD

CHD = CXD + HD; computer can be bought with or without hard drive
CXD = 1950 + HD; computer without the hard drive costs 1,950 dollars more than the hard drive alone
CHD = 2900; The computer with the hard drive costs 2,900

2900 = CXD + HD
1950 = CXD - HD
Two equations, two unknowns. Solve for HD by subtracting 2nd from the first equation
950 = 2HD
HD = 475

Posted: 08/07/2012 11:10
I'll admit I am probably missing something here.

I got the computer without the Hard drive CXD + HD = 2900. That makes total sense.

What I do not understand is why you would use CXD - HD for the computer without the hard drive.

This seems like an easy;
A = 1,950
B = 950
A+B = 2900

A + 0 = A

I do not see how it is implied that 1,950 is the cost of a computer plus the cost of a hard drive. It says that the computer without the hard drive is 1,950 more then the hard drive alone. How does that equate to the price of the computer without the hard drive plus the cost of the hard drive?

What am I missing here?
Posted: 08/07/2012 11:12
Computer with the hard drive = CXD + HD = 2,900. I made a mistake and typed without for some reason on that one.
Posted: 08/07/2012 11:21
A costs 10 more than B
Say, B is 20
A = B + 10 = 30
30 costs 10 more than 20

Cxd costs 1950 more than HD
Cxd = HD + 1950
Cxd - Hd = 1950
Posted: 08/07/2012 12:17
Wow, it finally clicked.

Thanks
Posted: 11/12/2014 18:41
I don't think the question tells us that CHD = CXD + HD. You assume it and it gets you to an answer. But you may well just assume the hard drive costs 400 and the higher priced combo package is all markup.

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